Chemistry and the Scientific Method | General Chemistry 1

Scientific method:

The scientific method is an empirical approach to problem-solving in science. It involves making observations, forming hypotheses, conducting experiments, collecting data, and drawing conclusions. Successful hypotheses may lead to the development of scientific theories.

Scientific notation:

Scientific notation is a way to express very large or very small numbers in a concise form.
In scientific notation, a number is written as N x 10ⁿ, where N is a number between 1 and 10, and n is a positive or negative integer.
 

850,000,000 = 8.5 x 10⁸ in scientific notation
0.0000023 = 2.3 x 10^-6 in scientific notation

States of matter:

Matter exists in three primary states: solid, liquid, and gas.

• Solids have a fixed volume and shape, with particles arranged in an ordered lattice.
• Liquids have a fixed volume but no specific shape, with particles free to move but held together by forces.
• Gases have neither fixed volume nor shape, with particles moving freely throughout the container.

Phase changes:

Phase changes involve the transition between different states of matter.

Matter can be classified as either a substance or a mixture.

• A substance has a definite composition and distinct properties, differing from other substances.
• A mixture consist of two or more substances, each retaining its identity, and can be homogeneous (uniform throughout) or heterogeneous. Mixtures can be separated using physical properties like filtration, distillation, or chromatography.

Chemistry and matter:

Chemistry is the study of matter and the changes it undergoes. Matter can be described by its properties, which may be quantitative (measured and expressed with a number) or qualitative (descriptive without numerical values).

Physical vs. chemical properties:

Physical properties can be observed or measured without changing the identity of the substance.
Chemical property is a property that are determined only as the result of a chemical process, where the original substance transforms into a new substance.
 

Physical properties: color, physical state, melting point, boiling point
Chemical properties: flammability, combustibility, oxidation states, enthalpy of formation

Intensive vs. extensive properties:

Intensive properties are independent of the amount of substance present.
Extensive properties are directly proportional to the amount of matter.
 

Intensive properties: density, color, temperature, hardness, melting point
Extensive properties: masse, volume, weight, length

SI base units

The International System of Units (SI) is the preferred system of units used in scientific work. SI units provide a standardized way to measure physical quantities and ensure consistency across scientific disciplines. There are seven fundamental SI base units:

• Length ⇒ meter = m
• Mass ⇒ kilogram = kg
• Temperature ⇒ kelvin = K
• Time ⇒ second = s
•  Electric current ⇒ ampere = A
• Amount of substance ⇒ mole = mol
• Luminous intensity ⇒ candela = cd

Prefixes used with SI units

Prefixes are used in the metric system to denote multiples or subdivisions of SI units. Common prefixes for SI units include:

Mass:

Mass is the amount of matter in an object and is measured in kilograms (kg) in the International System of Units (SI). One kilogram is equivalent to 2.205 pounds (lb).
Mass is distinct from weight, which is the force exerted by gravity on an object. Mass is constant regardless of an object's location, while weight varies depending on the gravitational field strength.
 

Length:

The meter (m) is the standard unit of length in the SI system. One meter is equivalent to 39.37 inches (in). The meter is defined as the distance traveled by light in a vacuum in 1/299,792,458 of a second.
 

Temperature (T)

Temperature can be measured in either the Kelvin scale (SI unit: K) or the Celsius scale (°C). The Kelvin scale is widely used in scientific contexts, while the Celsius scale is commonly used in everyday life. The relationship between Celsius and Kelvin temperatures is given by:

T (in K) = T (in °C) + 273.15

The Fahrenheit scale (°F) is also used, particularly in the United States, and the conversion from Celsius to Fahrenheit is:

T (in °F) = $\frac{9}{5}$ x T (in °C) + 32.0

Volume and density:

The derived SI unit for volume is the cubic meter (m³), but a more convenient measure is the liter (L).
1L = 1 dm³   and    1 m³ = 1000 L

Density (d) is the ratio of mass to volume and is typically expressed in kg.m^-3
 

Energy and power:

Energy (E) is the ability to cause a change in a physical system and is measured in joules (J), equivalent to kg.m².s^-2
The law of conservation of energy states that the total energy remains constant: E_total = E_k + E_p = constant

Kinetic Energy (E_k): energy associated with a moving object
 

Precision vs. accuracy:

• Precision refers to the degree of agreement between replicate measurements. It indicates how close these measurements are to each other.
• Accuracy refers to how close a measurement or result is to the true or accepted value. Percentage error can be used to measure accuracy:

Significant figures:

Significant figures are the meaningful digits in a measured or calculated value, representing the uncertainty of the measurement. Rules for determining significant figures include:

• Non-zero digits are always significant.
• Any zeros between two significant digits are significant.
• Zeros to the left of the first non-zero digit are not significant.
• Zeros to the right of the last non-zero digit are significant if the number contains a decimal point.
• Zeros to the right of the last non-zero digit in a number without a decimal point may or may not be significant ⇒ scientific notation should be used to avoid ambiguity in such cases.

0.051 has 2 significant figures
0.0510 has 3 significant figures
5.100 x 10³ has 4 significant figures

Exact numbers:

Exact numbers are quantities that can be counted or defined exactly, such as the number of objects. They have an infinite number of significant figures and do not limit the number of significant figures in a calculated result.
 

10 persons in a room ⇒ exact number ⇒ infinite number of significant figures

Addition and subtraction:

1. Count the number of significant figures in the decimal portion of each number.
2. Perform the addition or subtraction as usual.
3. The final answer cannot have more significant figures to the right of the decimal point than any of the original numbers.

5.05 – 3.229 = 1.821
5.05 ⇒ 2 digits after the decimal point
3.229 ⇒ 3 digits after the decimal point
The final answer cannot have more than 2 digits after the decimal point and is therefore rounded to 1.82 

Multiplication and division:

1. Count the number of significant figures of each number.
2. Perform the multiplication or division as usual.
3. The number of significant figures in the final answer is determined by the original number that has the smallest number of significant figures.

2.1 x 0.0568 = 0.11928
2.1 ⇒ 2 significant figures
0.0568 ⇒ 3 significant figures
The final answer must have 2 significant figures and is therefore rounded to 0.12

Conversion factor:

A conversion factor is a fraction where the same quantity is expressed in different units in the numerator and denominator, and it equals 1.
 

$\frac{3600 \mathrm{s}}{1 \mathrm{hour}}$ is the conversion factor to convert hours to seconds

Dimensional analysis:

Dimensional analysis involves using conversion factors to convert between different units while maintaining the same quantity. It ensures consistency and accuracy in calculations by manipulating quantities with their associated units.
 

Convert 2.0 m³ in liters:

Conversion factors: $\frac{1000 {\mathrm{dm}}^3}{1 {\mathrm{m}}^3}$ and $\frac{1 \mathrm{L}}{1 {\mathrm{dm}}^3}$

Dimensional analysis: 2.0 m³ x $\frac{1000 {\mathrm{dm}}^3}{1 {\mathrm{m}}^3}$ x $\frac{1 \mathrm{L}}{1 {\mathrm{dm}}^3}$ = 2000 L
Answer: 2.0 m³ = 2000 L

Convert 50 miles.hour^-1 in m.s^-1:

Conversion factors:  $\frac{1.61 \mathrm{km}}{1 \mathrm{mile}}$ ; $\frac{1000 \mathrm{m}}{1 \mathrm{km}}$ ; $\frac{1 \mathrm{hour}}{3600 \mathrm{s}}$

Dimensional analysis: 50 miles.hour^-1 = $\frac{50 \mathrm{miles}}{1 \mathrm{hour}}$ x $\frac{1.61 \mathrm{km}}{1 \mathrm{mile}}$ x $\frac{1000 \mathrm{m}}{1 \mathrm{km}}$ x $\frac{1 \mathrm{hour}}{3600 \mathrm{s}}$ = 22.4 m.s^-1

Answer: 50 miles.hour^-1 = 22.4 m.s^-1

Dimensional analysis method of problem solving:

1. Identify the given information, including units.
2. Identify the information needed in the answer, including units.
3. Find a relationship between the known information and needed answer and plan a strategy for conversion.
4. Solve the problem using dimensional analysis.
5. Check the reasonableness of the calculated answer with a rough estimate.